Consider integer coordinates x, y in the Cartesian plane and three functions f, g, h defined by:
f: 1 <= x <= n, 1 <= y <= n --> f...
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No loops required!
I'll put my thought process here because those equations look pretty arbitrary.
From that example grid of values of f, you can see the sum is 1*(n2 - (n-1)2) + 2 * ((n-1)2 - (n-2)2) + ... when you expand that out you get the sum of the first n squares. Which is the formula in
summin(that Google lead me to).For g, you can produce a chart of its value by taking an nxn square of n's, then subtracting the area of each square smaller than that. e.g. n*n*n - (n - 1)2 - (n - 2)2 -... which is the same as n*n*n - summin (n-1)
sumsum could be just the sum of the other two functions, but that's too simple. if you math it out, you get n*n*n + n*n. Much better.
Elegant challenge. We can notice that f and g are complementary to each other. We can draw the grid for f and g and notice, that sum of these grids is equal to sum of the gride of size n*n with (n+1) value is each cell. So the sum of f and g is equal to n*n*(n+1). The sum h is also equal to f + g.